Laying claim to culture is dumb? That's kinda how things have been for the past thousands of years. A lot of these cultures have existed longer than many modern countries have. Yes, they do have risks from a cultural extinction, but watering a culture down or disconnecting it from it's roots doesn't save it from extinction. If anything, it advances that. Having people of that culture continue their cultural practices and protecting those practices, helps ensure that culture continues on.
Yes, there can be an internet monoculture, but everyone is part of some subculture. And the subculture is what is being protected. These cultures have existed for hundreds or thousands of years, and they carry historical importance in understanding history and the evolution of society.